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Relations between input and output quantum states of integrated optical systems

Петер Адам, József Janszky, S. Szabo, E. Lugosi

Published Aug 29, 2016• 0 citations
OpenAlex

Abstract

Relations between the input and the output quasiprobability distribution functions, Glauber's R-functions, and photon number representations of the input and output density operators are found for a general optical four-port device.

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In this paper, we present a very simple approach to input-output relations in optical cavities, limiting ourselves to one- and two-photon states of the field. After field quantization, we derive the nonunitary transformation between inside and output annihilation and creation operators. Then we express the most general two-photon state generated by inside creation operators, through base states generated by output creation operators. After renormalization of coefficients of the inside two-photon state, we calculate the outside photon-number probability distribution in a general case; then we treat with some detail the single-mode and symmetrical cavity case. We found that the statistics of emitted photons may exhibit either quantum or classical behavior, depending both on source properties and on cavity characteristics.
A phase space for the single-mode light field is constructed by using optical phase variables. This phase-space formalism is directly connected to optical-phase-related operators. The phase-state basis \ensuremath{\Vert}\ensuremath{\theta}〉 is used to represent various quantum operators and states. Properties of the density operator \ensuremath{\rho}^ phase-state matrix elements P(\ensuremath{\theta},\ensuremath{\theta}')=〈\ensuremath{\theta}\ensuremath{\Vert}\ensuremath{\rho}^\ensuremath{\Vert}\ensuremath{\theta}'〉 and their relations to phase-related quasiprobability distributions are discussed. By using the phase representation, different types of number-phase intelligent states are analyzed.
The degenerate four-wave mixer is a nonlinear optical device capable of being configured to provide an extraordinarily broad range of photon statistics. The authors examine these statistics at its output in terms of the matrix representation of the process, which belongs to the SU(1,1) group of second-order unimodular matrices. The connection between this group and that of proper Lorentz transformations in two space dimensions and one time dimension permits the field density operators at the input and output ports of the device to be related by means of unitary transformations. This, in turn, provides the joint output photon number distribution for any joint input state.